# C.V.

Education

Graduate: University of Pennsylvania, Ph.D., 1991

Undergraduate: University of Pennsylvania, B.S., 1986

Academic Appointments

9/03 - Present: Professor, Loyola University Chicago

9/98 - 8/03: Associate Professor, Loyola University Chicago

9/97 - 5/98: Visiting Associate Professor: Texas A&M University

9/97 - 8/98: Associate Professor, Mississippi State University

9/95 - 8/97: Assistant Professor, Mississippi State University

9/91 - 8/95: Postdoctoral Assistant Professor: University of Michigan

Publications

An explicit deformation formula with noncommuting derivations, Ring theory (Ramat Gan and Jerusalem, 1988/1989), 396–403, Israel Math. Conf. Proc., 1, Weizmann, Jerusalem, 1989. (With V. Coll and M. Gerstenhaber)

Separable functors revisited. Comm. Algebra 18 (1990), no. 5, 1445–1459. (With F. Van Oystaeyen)

Quantization of tensor representations and deformation of matrix bialgebras. J. Pure Appl. Algebra 79 (1992), no. 2, 169–190.

Quantum symmetry. Quantum groups (Leningrad, 1990), 9–46, Lecture Notes in Math., 1510, Springer, Berlin, 1992. (With M. Gerstenhaber and S.D. Schack)

Quantum groups, cohomology, and preferred deformations. Proceedings of the XXth International Conference on Differential Geometric Methods in Theoretical Physics, Vol. 1, 2 (New York, 1991), 529–538, World Sci. Publ., River Edge, NJ, 1992. (With M. Gerstenhaber and S.D. Schack)

Construction of quantum groups from Belavin-Drinfelʹd infinitesimals. Quantum deformations of algebras and their representations (Ramat-Gan, 1991/1992; Rehovot, 1991/1992), 45–64, Israel Math. Conf. Proc., 7, Bar-Ilan Univ., Ramat Gan, 1993. (With M. Gerstenhaber and S.D. Schack)

Quantum Weyl algebras. J. Algebra 176 (1995), no. 3, 861–881. (With J.J. Zhang)

Boundary solutions of the classical Yang-Baxter equation. Lett. Math. Phys. 40 (1997), no. 4, 337–353. (With M. Gerstenhaber)

Nonstandard solutions of the Yang-Baxter equation. Lett. Math. Phys. 44 (1998), no. 1, 67–75. (With T. J. Hodges).

Bialgebra actions, twists, and universal deformation formulas. J. Pure Appl. Algebra 128 (1998), no. 2, 133–151. (With J.J. Zhang)

Boundary solutions of the quantum Yang-Baxter equation and solutions in three dimensions. Lett. Math. Phys. 44 (1998), no. 2, 131–141. (With M. Gerstenhaber)

Compatible deformations. Trends in the representation theory of finite-dimensional algebras (Seattle, WA, 1997), 159–168, Contemp. Math., 229, Amer. Math. Soc., Providence, RI, 1998. (With M. Gerstenhaber)

Generators and relations for Schur algebras. Electron. Res. Announc. Amer. Math. Soc. 7 (2001), 54–62 (electronic). (With S. Doty)

The Donald-Flanigan problem for finite reflection groups. EuroConférence Moshé Flato 2000, Part I (Dijon). Lett. Math. Phys. 56 (2001), no. 1, 41–72. (With M. Gerstenhaber and M. Schaps)

Presenting Schur algebras. Int. Math. Res. Not. 2002, no. 36, 1907–1944. (With S. Doty)

Algebraic deformations arising from orbifolds with discrete torsion. J. Pure Appl. Algebra 187 (2004), no. 1-3, 51–70. (With A. Căldăraru and S. Witherspoon)

Presenting Schur algebras as quotients of the universal enveloping algebra of gl(2). Algebr. Represent. Theory 7 (2004), no. 1, 1–17. (With S. Doty)

Quantum groups and deformation quantization: explicit approaches and implicit aspects. J. Math. Phys. 45 (2004), no. 10, 3703–3741. (With P. Bonneau, M. Gerstenhaber and D. Sternheimer)

Diagrams of Lie algebras. J. Pure Appl. Algebra 196 (2005), no. 2-3, 169–184. (With M. Gerstenhaber and S.D. Schack)

Presenting generalized Schur algebras in types B, C, and D. Adv. Math. 206 (2006), no. 2, 434–454. (With S. Doty and J. Sullivan)

On the defining relations for generalized q-Schur algebras. Adv. Math. 221 (2009), no. 3, 955–982. (With S. Doty and J. Sullivan)

The principal element of a Frobenius Lie algebra. Lett. Math. Phys. 88 (2009), no. 1-3, 333–341.

Topics in algebraic deformation theory. Higher Structures in Geometry and Physics, 1-24, Progress in Mathematics 287, Springer, New York, 2010.

Meander graphs and Frobenius seaweed algebras (with V. Coll and C. Magnant), Journal of Generalized Lie Theory, 5, (2011), 1 - 7 (With V. Coll and C. Magnant).

On the cohomology of the Weyl algebra, the quantum plane, and the q-Weyl algebra, Journal of Pure and Applied algebra 218 (2014), 879-887. (With M. Gerstenhaber)

Deformations associated with rigid algebras, Journal of Homotopy and Related Structures (2014), in press.

Cellular bases of generalized q-Schur algebras(with S. Doty, Mathematical Proceedings of the Cambridge Philosophical Society, 162, (2017), 533-560.

The Collaborative Development of Active Learning at Loyola University Chicago as Part of the SEMINAL Network, PRIMUS 31, no 3-5 (2021), 281- 295.

Peter-Weyl bases, preferred deformations and Schur-Weyl duality (with A. Gillman and P. Tingley), Representation Theory, Mathematical Physics, and Integrable Systems, Progress in Mathematics 340, https://doi.org/10.1007/978-3-030-78148-4_9.

Schur-Weyl Duality for Tensor Powers of the Burau Representation (with S. Doty), Res Math Sci 8, 47 (2021). https://doi.org/10.1007/s40687-021-00282-3.

Schur-Weyl Duality for Twin Groups (with S. Doty), Transformation Groups (2022). https://doi.org/10.1007/s00031-022- 09708-w

The Partial Temperley-Lieb Algebra and its Representations (with S. Doty), Journal of Combinatorial Algebra, (7), 2023, no. 3/4, pp 401-439.

An orthogonal realization of representations of the Temperley–Lieb algebra (with S. Doty), Journal of Algebra, (655), 2024, no. 1, pp 394-432.

Origins of the Temperley-Lieb Algebra: Early History, preprint, (with S. Doty) , arXiv:2307.11929, 2023.

Edited Books

Higher Structures in Geometry and Physics, Progress in Mathematics 287, Springer, New York, 2010. xv+362pp. (A. Cattaneo, A. Giaquinto, and P. Xu, eds.)